Titlebook: Random Coefficient Autoregressive Models: An Introduction; An Introduction Des F. Nicholls,Barry G. Quinn Book 1982 Springer-Verlag New Yor

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Maximum Likelihood Estimation of Scalar Models,and {B(t)} were sequences of normally distributed random variables. We shall refer to the estimates obtained in this way as maximum likelihood estimates even though it will be shown that these estimates will be strongly consistent and satisfy a central limit theorem if the processes {ε(t)} and ({B(t

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A Monte Carlo Study, models for several sets of data of different sizes. While the simulations performed have been by no means exhaustive, as we shall see the results do conform with the asymptotic theory developed in the last two chapters.

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Testing the Randomness of the Coefficients,The condition (cii), however, which was assumed so as to obtain a standard central limit theorem for the maximum likelihood estimates, precludes the use of the theory derived in chapter 4 to test what is perhaps the most relevant hypothesis, namely that Σ = 0, that is, that the data come from a fixe